In this paper,we address matrix-valued distributed stochastic optimization with inequality and equality constraints,where the objective function is a sum of multiple matrix-valued functions with stochastic variables a...In this paper,we address matrix-valued distributed stochastic optimization with inequality and equality constraints,where the objective function is a sum of multiple matrix-valued functions with stochastic variables and the considered problems are solved in a distributed manner.A penalty method is derived to deal with the constraints,and a selection principle is proposed for choosing feasible penalty functions and penalty gains.A distributed optimization algorithm based on the gossip model is developed for solving the stochastic optimization problem,and its convergence to the optimal solution is analyzed rigorously.Two numerical examples are given to demonstrate the viability of the main results.展开更多
基金Project supported by the National Natural Science Foundation of China(No.62173308)the Natural Science Foundation of Zhejiang Province,China(Nos.LR20F030001 and LD19A010001)the Jinhua Science and Technology Project,China(No.2022-1-042)。
文摘In this paper,we address matrix-valued distributed stochastic optimization with inequality and equality constraints,where the objective function is a sum of multiple matrix-valued functions with stochastic variables and the considered problems are solved in a distributed manner.A penalty method is derived to deal with the constraints,and a selection principle is proposed for choosing feasible penalty functions and penalty gains.A distributed optimization algorithm based on the gossip model is developed for solving the stochastic optimization problem,and its convergence to the optimal solution is analyzed rigorously.Two numerical examples are given to demonstrate the viability of the main results.
